What units are the hair particles' diameter are measured in?
Cycles hair particle size units, like most other settings in Blender are expressed in Blender scene units.

The Scaling parameter is the actual width of the hair in scene units. The confusion might stem from the fact that on top there are scaling factors applied that may induce doubt.

Setting a Scaling value to $1$ and leaving the Root at $1$ and Tip at $0$ will yield a hair particle of length $N$ (set in the length property at the top) that is exactly $1$ Blender unit wide at the root, and progress to zero width at the tip.

Tip and Root are scaling factors applied to the base Scaling property, having a root value of $0.5$ over a Scaling of $1$ will lead to a root of $0.5$ Blender units. Likewise having Tip at $0.2$ will yield a hair particle with $0.2$ BU at the end.

The Shape property will control how the width shape progresses from root to the tip.

Here we se a single hair particle with $1$ unit of lenghth applied over a $1\text{ x }1$ plane, and starting with a Scaling of $1$, Root of $1$ and Tip at $0$.